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Volume 31, Issue 3
Global Existence and Blow Up of Solutions in a Cauchy Viscoelastic Problem

Gongwei Liu & Shuying Tian

DOI: 10.4208/jpde.v31.n3.3

J. Part. Diff. Eq., 31 (2018), pp. 224-236.

Published online: 2018-09

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  • Abstract

The Cauchy problem for a viscoelastic equation with nonlinear damping and source terms is considered. We establish the nonexistence result of global solutions with initial energy controlled above by a critical value by modifying the method introduced in a work by Autuori et al. in 2010. Then we establish global existence for arbitrary initial data or the energy in potential well. These improve earlier results in the literatures.

  • Keywords

Cauchy problem viscoelastic equation global existence blow up.

  • AMS Subject Headings

35B44, 35L05, 35R09, 45K05

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

gongweiliu@126.com (Gongwei Liu)

sytian@whut.edu.cn (Shuying Tian)

  • BibTex
  • RIS
  • TXT
@Article{JPDE-31-224, author = {Liu , Gongwei and Tian , Shuying}, title = {Global Existence and Blow Up of Solutions in a Cauchy Viscoelastic Problem}, journal = {Journal of Partial Differential Equations}, year = {2018}, volume = {31}, number = {3}, pages = {224--236}, abstract = {

The Cauchy problem for a viscoelastic equation with nonlinear damping and source terms is considered. We establish the nonexistence result of global solutions with initial energy controlled above by a critical value by modifying the method introduced in a work by Autuori et al. in 2010. Then we establish global existence for arbitrary initial data or the energy in potential well. These improve earlier results in the literatures.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v31.n3.3}, url = {http://global-sci.org/intro/article_detail/jpde/12706.html} }
TY - JOUR T1 - Global Existence and Blow Up of Solutions in a Cauchy Viscoelastic Problem AU - Liu , Gongwei AU - Tian , Shuying JO - Journal of Partial Differential Equations VL - 3 SP - 224 EP - 236 PY - 2018 DA - 2018/09 SN - 31 DO - http://doi.org/10.4208/jpde.v31.n3.3 UR - https://global-sci.org/intro/article_detail/jpde/12706.html KW - Cauchy problem KW - viscoelastic equation KW - global existence KW - blow up. AB -

The Cauchy problem for a viscoelastic equation with nonlinear damping and source terms is considered. We establish the nonexistence result of global solutions with initial energy controlled above by a critical value by modifying the method introduced in a work by Autuori et al. in 2010. Then we establish global existence for arbitrary initial data or the energy in potential well. These improve earlier results in the literatures.

Gongwei Liu & Shuying Tian. (2019). Global Existence and Blow Up of Solutions in a Cauchy Viscoelastic Problem. Journal of Partial Differential Equations. 31 (3). 224-236. doi:10.4208/jpde.v31.n3.3
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